226 ASTRONOMY. 



(*) III. That the subsisting law of attraction falls 

 within the limits which utility requires, when these limits 

 bear so small a proportion to the range of possibilities, upon 

 which chance might equally have cast it, is not, with any 

 appearance of reason, to be accounted for, by any other 

 cause than a regulation proceeding from a designing mind. 

 But our next proposition carries the matter somewhat fur- 

 ther. We say, in the third place, that, out of the different 

 laws which lie within the limits of admissible laws, the 

 best is made choice of; that there are advantages in this 

 particular law which cannot be demonstrated to belong 

 to any other law ; and concerning some of which, it can 

 be demonstrated that they do not belong to any other. 



(*) 1. Whilst this law prevails between each particle 

 of matter, the united attraction of a sphere, composed of 

 that matter, observes the same law. This property of the 

 law is necessary, to render it applicable to a system com- 

 posed of spheres, but it is a property which belongs to no 

 other lav/ of attraction that is admissible. The law of va- 

 riation of the united attraction is in no other case the same 

 as the law of attraction of each particle, one case excepted, 

 and that is of the attraction varying directly as the distance ; 

 the inconveniency of which law in other respects we have 

 already noticed.* 



We may follow this regulation somewhat farther, and still 

 more strikingly perceive that it proceeded from a designing 

 mind. A law both admissible and convenient was requisite. 

 In what way is the law of the attracting globes obtained? 

 Astronomical observations and terrestrial experiments show 

 that the attraction of the globes of the system is made up of 

 the attraction of their parts ; the attraction of each globe 

 being compounded of the attraction of its parts. Kovv, the 

 admissible and convenient law which exists, could not: be ob- 

 tained in a system of bodies gravitating by the united grav- 

 itation of their parts, unless each particle of matter were 

 attracted by a force varying by one particular law, viz. va- 

 rying inversely as the square of the distance ; for, if the ac- 

 tion of the particles be according to any other law what- 

 ever, the admissible and convenient law which is adopted 



*Let A, Fig. 5, Plate XXXIX, represent a sphere composed of par- 

 ticles, which mutually attract each other with a force, which varies 

 reciprocally as the squares of the distances ; their uuited attraction, on 

 a similar particle P without the sphere, will be according to the same 

 law ; that is, the particle will be attracted towards the sphere with a 

 force which will also vary reciprocally as the square of C P, its dis- 

 tance from the centre of the sphere. Paxton. 



